Interest rate swap compression

ABSTRACT

A computer system may access data corresponding to a portfolio that comprises interest rate swaps and may calculate parameters for a compressed swap. The computer system may determine, based at least in part on the parameters for the compressed swap, a performance bond requirement attributable to the interest rate swaps. The computer system may compare the performance bond requirement to account data associated with a holder of the portfolio and may perform one or more additional actions based on the comparing.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation under 37 C.F.R. § 1.53(b) of U.S.Pat. Application Ser. No. 17/020,423 filed Sep. 14, 2020 now U.S. Pat.No. , which is a continuation under 37 C.F.R. § 1.53(b) of U.S. Pat.Application Ser. No. 14/750,422 filed Jun. 25, 2015 now U.S. Pat. No.10,810,671, which claims the benefit of the filing date under 35 U.S.C.§ 119(e) U.S. Provisional Pat. Application Serial No. 62/018,272, filedJun. 27, 2014, the entire disclosures of which are hereby incorporatedby reference.

BACKGROUND

An interest rate swap is a type of over-the-counter (OTC) product inwhich parties agree to exchange streams of future interest paymentsbased on a specified principal or notional amount. Each stream may bereferred to as a leg. Swaps are often used to hedge certain risks, butthey may also be used for speculative purposes.

An example of an interest rate swap includes a plain fixed-to-floating,or “vanilla,” swap. A vanilla swap includes an exchange of an intereststream based on a floating rate and an interest stream based on a fixedrate. In a vanilla swap, a first party makes periodic interest paymentsto a second party based on the floating interest rate and receivesinterest payments from the second party based on the fixed interestrate. Conversely, the second party receives periodic interest paymentsfrom the first party based on the floating interest rate and makesinterest payments to the first party based on the fixed interest rate.The fixed and floating rate payments are based on a common notionalamount. Over the life of the swap, the floating rate may be periodicallyreset to a rate published by a known source of short-term interestrates, e.g., the London InterBank Offered Rate (LIBOR).

Streams of payments under a swap may extend well into the future (e.g.,10 years or more). Parties may accumulate large portfolios of swaps. Assuch, financial institutions, such as a financial exchange, a bank, aninvestment broker, etc. may face an increased need for data storageand/or computing capacity to manage one or more of these largeportfolios of swaps. For various reasons, it would be desirable tocondense multiple swaps in a portfolio into a single hypothetical swapthat has characteristics similar to the portfolio swaps.

SUMMARY

This Summary is provided to introduce a selection of concepts in asimplified form that are further described below in the DetailedDescription. This Summary is not intended to identify key features oressential features of the invention.

In some embodiments, a computer system may access data corresponding toa portfolio that comprises m interest rate swaps, wherein m is aninteger greater than one. A financial institution managing the portfoliomay have a first data storage capacity large enough to store informationassociated with the portfolio comprising m interest rate swaps. Theaccessed data may comprise, for each of the interest rate swaps, anotional value and a fixed rate value. Each of the interest rate swapsmay correspond to a common tenor. The computer system may calculateparameters for a compressed swap having a risk value equivalent to a sumof risk values of the interest rate swaps. The parameters may include acompressed swap notional value N_(B), a compressed swap fixed rate valuex_(B), and a compressed swap floating rate spread value c. The computersystem may optionally determine, based at least in part in thecompressed swap parameters, a performance bond requirement attributableto the interest rate swaps. The computer system may compare a determinedperformance bond requirement to account data associated with a holder ofthe portfolio and may perform one or more additional actions based onthe comparing.

A financial institution associated with the portfolio may have one ormore computing systems (e.g., servers, data repositories, processors,etc.) that may be used, at least in part, to store or otherwise manageportfolios of the financial institution’s clients. These financialinstitution computing systems may be sized to manage a specified amountof data associated with aspects of the financial institution’s business.This may include managing and/or processing information associated withthe portfolios. As portfolios become larger for one or more of thefinancial institution’s clients, the data storage capacity and/orprocessing power necessary to process and/or store this information mayapproach a storage capacity and/or processing power limit of thecurrently installed hardware. As such, the financial institution may berequired to install more computing devices and/or upgrade existingcomputing components to handle the additional information storage and/orprocessing requirements. By monitoring, or otherwise managing the sizeof one or more portfolios, the financial institution may be able toproactively manage the computing requirements and the associated costs.For example, the financial institution may monitor a size of a client’sportfolio. If the portfolio size approaches a threshold, the financialinstitution computing system may automatically initiate a portfoliocompression process. In other cases, the financial institution computingsystem may provide an indication to an individual, such as a networkmanager, that the computing system is approaching the limits to allowmanual initiation of a portfolio compression process. Alternatively, thecomputing system may store the portfolio in a compressed form for someor all clients so as to minimize the data storage and processingrequirements.

Embodiments include, without limitation, methods for compressinginterest rate swaps, computer systems configured to perform such methodsand non-transitory computer-readable media storing instructionsexecutable by a computer system to perform such methods.

BRIEF DESCRIPTION OF THE DRAWINGS

Some embodiments are illustrated by way of example, and not by way oflimitation, in the figures of the accompanying drawings and in whichlike reference numerals refer to similar elements.

FIG. 1 shows an exemplary trading network environment for implementingtrading systems and methods according to at least some embodiments.

FIG. 2 is a flow chart showing operations performed, according to someembodiments, in connection with calculating parameters for ahypothetical condensed swap.

FIG. 3 is a chart showing swap curve data for an example set of swaps.

FIG. 4 is a flow chart showing operations performed, according to someadditional embodiments, in connection with calculating parameters for ahypothetical condensed swap.

DETAILED DESCRIPTION

In the following description of various embodiments, reference is madeto the accompanying drawings, which form a part hereof, and in whichvarious embodiments are shown by way of illustration. It is to beunderstood that there are other embodiments and that structural andfunctional modifications may be made. Embodiments of the presentinvention may take physical form in certain parts and steps, examples ofwhich will be described in detail in the following description andillustrated in the accompanying drawings that form a part hereof.

Various embodiments may comprise a method, a computer system, and/or acomputer program product. Accordingly, one or more aspects of one ormore of such embodiments may take the form of an entirely hardwareembodiment, an entirely software embodiment and/or an embodimentcombining software and hardware aspects. Furthermore, such aspects maytake the form of a computer program product stored by one or morenon-transitory computer-readable storage media having computer-readableprogram code, or instructions, embodied in or on the storage media. Theterms “computer-readable medium” and “computer-readable storage medium”as used herein include not only a single medium or single type ofmedium, but also a combination of one or more media and/or types ofmedia. Such a non-transitory computer-readable medium may storecomputer-readable instructions (e.g., software) and/or computer-readabledata (i.e., information that may or may not be executable). Any suitablecomputer readable media may be utilized, including various types ofnon-transitory computer readable storage media such as hard disks,CD-ROMs, optical storage devices, magnetic storage devices, FLASH memoryand/or any combination thereof. The terms “computer-readable medium” and“computer-readable storage medium” could also include an integratedcircuit or other device having hard-coded instructions (e.g., logicgates) that configure the device to perform one or more operations.

Aspects of method steps described in connection with one or moreembodiments may be executed by one or more processors associated with acomputer system (such as exchange computer system 100 described below).As used herein, a “computer system” could be a single computer or couldcomprise multiple computers. When a computer system comprising multiplecomputers performs a method, various steps could be performed bydifferent ones of those multiple computers. Processors of a computersystem may execute computer-executable instructions stored onnon-transitory computer-readable media. Embodiments may also bepracticed in a computer system forming a distributed computingenvironment, with tasks performed by remote processing devices that arelinked through a communications network. In a distributed computingenvironment, program modules may be located in both local and remotecomputer storage media including memory storage devices.

Exemplary Operating Environment

Aspects of at least some embodiments can be implemented with computersystems and computer networks that allow users to communicate tradinginformation. An exemplary trading network environment for implementingsystems and methods according to at least some embodiments is shown inFIG. 1 . The implemented systems and methods can include systems andmethods, such as are described herein, that facilitate data processingand other activities associated with compressing interest rate swaps.

Computer system 100 can be operated by a financial product exchange andconfigured to perform operations of the exchange for, e.g., trading andotherwise processing various financial products. Financial products ofthe exchange may include, without limitation, futures contracts, optionson futures contracts, other types of options, and other types ofderivative contracts. Financial products traded or otherwise processedby the exchange may also include over-the-counter (OTC) products such asforwards, OTC options, interest rate swaps, etc. Financial productstraded through the exchange may also or alternatively include othertypes of financial interests, including without limitation stocks, bondsand or other securities (e.g., exchange traded funds), foreigncurrencies, and spot market trading of commodities.

Computer system 100 receives orders for financial products, matchesorders to execute trades, transmits market data related to orders andtrades to users, and performs other operations associated with afinancial product exchange. Exchange computer system 100 may beimplemented with one or more mainframe, desktop or other computers. Inone embodiment, a computer device uses a 64-bit processor. A userdatabase 102 includes information identifying traders and other users ofexchange computer system 100. Data may include user names and passwords.An account data module 104 may process account information that may beused during trades. A match engine module 106 is included to matchprices and other parameters of bid and offer orders. Match engine module106 may be implemented with software that executes one or morealgorithms for matching bids and offers.

A trade database 108 may be included to store information identifyingtrades and descriptions of trades. In particular, a trade database maystore information identifying the time that a trade took place and thecontract price. An order book module 110 may be included to store pricesand other data for bid and offer orders, and/or to compute (or otherwisedetermine) current bid and offer prices. A market data module 112 may beincluded to collect market data, e.g., data regarding current bids andoffers for futures contracts, futures contract options and otherderivative products, swap curve data, etc. Module 112 may also preparethe collected market data for transmission to users. A risk managementmodule 134 may be included to compute and determine a user’s riskutilization in relation to the user’s defined risk thresholds. An orderprocessor module 136 may be included to decompose delta based and bulkorder types for further processing by order book module 110 and matchengine module 106.

A clearinghouse module 140 may be included as part of exchange computersystem 100 and configured to carry out operations of a clearinghouse ofthe exchange that operates computer system 100. Module 140 may receivedata from and/or transmit data to trade database 108 and/or othermodules of computer system 100 regarding trades of futures contracts,futures contracts options, swaps, and other financial products tradedthrough the exchange that operates system 100. Clearinghouse module 140may facilitate the financial product exchange (or a clearinghouse of theexchange) acting as one of the parties to every traded contract or otherproduct. For example, parties A and B may agree, either bilaterally orby matching of orders submitted to computer system 100, to becomecounterparties to a swap or other type of financial product. Module 140may then create an exchange-traded financial product between party A andthe exchange clearinghouse and a second exchange-traded financialproduct between the exchange clearinghouse and party B. Module 140 maysimilarly create offsetting contracts when creating contracts as aresult of an option exercise and/or may select option grantors tofulfill obligations of exercising option holders. Module 140 may also beconfigured to perform other clearinghouse operations. As a furtherexample, module 140 may maintain margin data with regard to clearingmembers and/or trading customers. As part of such margin-relatedoperations, module 140 may store and maintain data regarding the valuesof various options, futures contracts and other interests, determinemark-to-market and final settlement amounts, confirm receipt and/orpayment of amounts due from margin accounts, confirm satisfaction ofdelivery and other final settlement obligations, etc.

Each of modules 102 through 140 could be implemented as separatesoftware components executing within a single computer, separatehardware components (e.g., dedicated hardware devices) in a singlecomputer, separate computers in a networked computer system, or anycombination thereof (e.g., different computers in a networked system mayexecute software modules corresponding more than one of modules102-140). When one or more of modules 102 through 140 are implemented asseparate computers in a networked environment, those computers may bepart of a local area network, a wide area network, and/or multipleinterconnected local and/or wide area networks.

Exchange computer system 100 may also communicate in a variety of wayswith devices that may be logically distinct from computer system 100.For example, computer device 114 is shown directly connected to exchangecomputer system 100. Exchange computer system 100 and computer device114 may be connected via a T1 line, a common local area network (LAN) orother mechanism for connecting computer devices. Also shown in FIG. 1 isa radio 132. The user of radio 132 (e.g., a trader or exchange employee)may transmit orders or other information to a user of computer device114. The user of computer device 114 may then transmit those orders orother information to exchange computer system 100 using computer device114.

Computer devices 116 and 118 are coupled to a LAN 124 and maycommunicate with exchange computer system 100 via LAN 124. LAN 124 mayimplement one or more of the well-known LAN topologies and may use avariety of different protocols, such as Ethernet. Computers 116 and 118may communicate with each other and other computers and devicesconnected to LAN 124. Computers and other devices may be connected toLAN 124 via twisted pair wires, coaxial cable, fiber optics, radio linksor other media.

A wireless personal digital assistant device (PDA) 122 may communicatewith LAN 124 or the Internet 126 via radio waves. PDA 122 may alsocommunicate with exchange computer system 100 via a conventionalwireless hub 128. As used herein, a PDA includes mobile telephones andother wireless devices that communicate with a network via radio waves.

FIG. 1 also shows LAN 124 connected to the Internet 126. LAN 124 mayinclude a router to connect LAN 124 to the Internet 126. Computer device120 is shown connected directly to the Internet 126. The connection maybe via a modem, DSL line, satellite dish or any other device forconnecting a computer device to the Internet. Computers 116, 118 and 120may communicate with each other via the Internet 126 and/or LAN 124.

One or more market makers 130 may maintain a market by providingconstant bid and offer prices for a derivative or security to exchangecomputer system 100. Exchange computer system 100 may also include tradeengine 138. Trade engine 138 may, e.g., receive incoming communicationsfrom various channel partners and route those communications to one ormore other modules of exchange computer system 100.

One skilled in the art will appreciate that numerous additionalcomputers and systems may be coupled to exchange computer system 100.Such computers and systems may include, without limitation, additionalclearing systems, regulatory systems and fee systems.

The operations of computer devices and systems shown in FIG. 1 anddescribed herein may be controlled by computer-executable instructionsstored on one or more non-transitory computer-readable media. Forexample, computer device 116 may include computer-executableinstructions for receiving market data from exchange computer system 100and displaying that information to a user. As another example, module140 and/or other modules of exchange computer system 100 may include oneor more non-transitory computer-readable media storingcomputer-executable instructions for performing herein-describedoperations.

Of course, numerous additional servers, computers, handheld devices,personal digital assistants, telephones and other devices may also beconnected to exchange computer system 100. Moreover, one skilled in theart will appreciate that the topology shown in FIG. 1 is merely anexample and that the components shown in FIG. 1 may be connected bynumerous alternative topologies.

Exemplary Embodiments

In at least some embodiments, exchange computer system 100 (or “computersystem 100”) receives, stores, generates and/or otherwise processes datain connection with compressing interest rate swaps in a portfolio. Forconvenience, the term “swap” is used herein as a shorthand reference toan interest rate swap.

Large portfolios of swaps are common, and a party may enter into one ormore swaps to hedge positions in one or more markets. Generally, anavailable fixed rate dictates the price of a swap. The fixed rate atwhich a swap might be entered generally changes over time. For example,a dealer may quote a swap at a first fixed rate at a time 0. A shorttime later, the same dealer may provide a quote for a similar swap, buthaving a second fixed rate that is different than the first fixed rate.Once a swap is entered, the fixed rate will remain fixed for thelifetime of the swap. Over time, party may develop a portfolio of swaps.In some of those swaps, the party may pay the fixed rate leg of theswap. In others of those swaps the party may pay the floating rate legof the swap. Typically, few or no swaps in a portfolio have the samefixed interest rates. As a result, few (if any) of those swaps net out,and a large number of swap positions remain open on the accountingdatabase associated with the party holding those swap positions.

A large number of swaps can result in a substantial performance bondrequirement, even if such swaps are roughly split between swaps in whichthe portfolio holder pays the fixed rate and swaps in which theportfolio holder receives the fixed rate. For example, a portfolio mayinclude a first swap in which the portfolio holder pays fixed rate R1 ona $100 million notional and a second swap in which the portfolio holderreceives fixed rate R2 on a $100 million notional. Because R1 ≠ R2,these swaps do not net out, and a performance bond requirement for theportfolio may be calculated based on the $200 million gross notionalamount.

In some embodiments, a computer system may analyze multiple swaps in aportfolio. Based on that analysis, the computer system may thencalculate parameters of a single hypothetical compressed swap that hasvalues for one or more risk metrics that are equivalent to a sum (orsums) of such risk metrics for the actual swaps, and that has a netpresent value equivalent to the combined net present values of theactual swaps. A performance bond requirement for the hypotheticalcompressed swap may be lower than a performance bond requirementcalculated based on the actual swaps.

FIG. 2 is a flow chart showing operations performed by computer system100, according to some embodiments, in connection with calculatingparameters for a hypothetical condensed swap. The following descriptionof some embodiments refers to operations performed by clearinghousemodule 140. In other embodiments, however, some or all of theseoperations may be performed by other modules of computer system 100and/or by modules of one or more other computer systems.

In step 201, module 140 accesses data corresponding a portfolio thatincludes m swaps, where m is an integer greater than one. For each ofthe m swaps, a first counterparty (“fixed payor”) makes payments at afixed interest rate payment based on a swap notional amount and receivespayments at a floating interest rate based on that same notional amount,while a second counterparty (“fixed receiver”) receives payments at thefixed interest rate based on that notional amount and makes payments atthe floating rate based on that notional amount. The notional and/or thefixed rate may be different for some or all of the m swaps. For some ofthe m swaps, the portfolio holder may be the fixed payor, while inothers the portfolio holder may be the fixed receiver. The floating ratein each of the m swaps may be based on the same source, e.g., the LondonInterBank Offered Rate. The data accessed in step 201 may include, foreach of the m swaps, the nature of the portfolio holder position (fixedpayor or fixed receiver), the notional amount, the fixed rate, thesource of the floating rate, the tenor of the swap (e.g., the date onwhich the final fixed and floating payments are due), the fixed andfloating payment dates, etc. In some embodiments, a single tenor iscommon to all of the m swaps. Table 1 includes information for fifteenswaps (m=15) according to one example.

TABLE 1 Swap no. Fixed rate, per annum (%) Notional ($) 1 3 -100,000,0002 3.5 99,000,000 3 3.1 -1,200,000 4 2.9 15,600,000 5 3.101 30,000,000 63.2 16,500,000 7 2.9545 33,470,000 8 3.241 20,000,000 9 3.2254-1,500,000 10 3.4591 45,000,000 11 3.0125 -17,250,000 12 3.225165,432,100 13 2.1975 -87,542,100 14 1.841 -155,210,000 15 3.1478-38,210,000

In the example of Table 1, each of the swaps has a 10 year tenor andends on May 13, 2024. The floating rate for each swap is the 3-monthLIBOR. A negative value for notional amount indicates a fixed rate payorposition in a swap. A positive value for notional amount indicates afixed rate receiver position in a swap.

As part of step 201, module 140 may access other data that includesadditional values associated with the m swaps. Such additional data mayinclude, e.g., a swap curve. Swap curves and methods of generating datafor swap curves are well known. FIG. 3 is a chart that includes swapcurve data for the example swaps of Table 1. Column 301 identifiessettlement dates on which fixed and/or floating payments are made. Forthe example swaps of Table 1, it is assumed that fixed rate payments aremade semi-annually (e.g., on Nov. 12, 2014, on May 12, 2015, on Nov. 12,2015, etc.) and that floating rate payments are made quarterly (e.g., onAug. 12, 2014, on Nov. 12, 2014, on Feb. 12, 2015, on May 12, 2015,etc.). Each row in FIG. 3 thus represents a different floating ratepayment period. Column 302 includes year fractions applicable to each ofthe floating rate payment periods. Because of weekends and/or holidaysthat may require postponement of a settlement date until a next businessday, and because some months are shorter than others, some floating ratepayment periods are slightly less than or greater than a quarter of ayear. Column 303 includes floating rates applicable to each of thefloating rate payment periods. For example, the floating rate applicableto the floating rate payment period settling Aug. 12, 2014 is shown inFIG. 3 as 0.23%. The rates are indicated in column 303 in a per annumformat. Column 304 includes discount factors applicable to each of thefloating rate payment periods.

In step 202, module 140 calculates parameters for a hypotheticalcompressed swap based on the m swaps. In at least some embodiments, thecompressed swap may have a hypothetical present value that is equivalentto the combined present values of the m swaps. As used herein,“equivalent” means equal or nearly equal (e.g., plus or minus a fewpercent). The compressed swap may also or alternatively havecorresponding values for risk-related metrics that are equivalent to thesums of those risk metric values corresponding to the m swaps.

The parameters calculated in step 202 may include a compressed swapnotional value N_(B), a compressed swap fixed rate value x_(B), and acompressed swap floating rate spread value c. In some embodiments, thecompressed swap has the common tenor of the m swaps. If N_(B) ispositive, the portfolio holder is assumed to receive payments under thecompressed swap at fixed rate x_(B) based on notional N_(B) and to makefloating rate payments, based on notional N_(B), at a floating rate thatis greater than the floating rate of the m swaps by an amount c (e.g.,the applicable LIBOR increased by c). If N_(B) is negative, theportfolio holder is assumed to make payments at fixed rate x_(B) basedon notional N_(B) and to receive floating rate payments, based onnotional N_(B), at a floating rate that is greater than the floatingrate of the m swaps by an amount c. In some embodiments, x_(B), N_(B),and c are calculated according to Equations 1 through 3.

$x_{B} = \frac{1}{m}{\sum\limits_{j = 1}^{m}x_{j}}$

$N_{B} = \frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{x_{B}}$

$c = \frac{1}{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\left\lbrack {\frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}} - {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right\rbrack$

In Equations 1 through 3, and in subsequently described equations andinequalities, m is the number of swaps for which data was accessed instep 1, j is an index to one of the m swaps, x_(j) is the fixed ratevalue for the j^(th) swap, N_(j) is the notional of the j^(th) swap, Gis the number of floating rate payment periods, g is an index to one ofthe G floating rate payment periods, f_(g) is the floating rateapplicable to the g^(th) floating rate payment period, df_(g) is thefloating rate discount factor applicable to the g^(th) floating ratepayment period, and dt_(g) is the duration of the g^(th) floating ratepayment period. The derivation of Equation 3 is explained below. As alsoexplained below, a compressed swap having parameters x_(B), N_(B), and ccalculated according to Equations 1 through 3 has a present valueequivalent to the combined present values of the m swaps.

Returning to the example swaps of Table 1, and using the correspondingswap curve data in FIG. 3 , a hypothetical compressed swap has an x_(B)value of 3.007%, an N_(B) value of $143,511,976, and c value of 0.556%.Under that compressed swap, the portfolio holder would be assumed toreceive fixed rate payments at a rate of 3.007% based on a $143,511,976notional and to make floating rate payments at LIBOR + c based on that$143,511,976 notional. As shown below in Table 2, the net present valueof that compressed swap (CS) is equivalent to the sum of the net presentvalues of the swaps.

TABLE 2 Swap NPV ($) DV01 CV01 1 -2,898,889.57 -91,649.84 -871,394 27,382,323.11 93,003.96 877,801 3 -45,725.88 -1,105.30 -10,493 4310,017.10 14,225.82 135,461 5 1,145,881.82 27,633.94 262,344 6779,144.94 15,273.60 144,788 7 831,432.07 30,605.35 291,190 81,019,169.35 18,551.07 175,751 9 -74,304.56 -1,390.26 -13,174 103,187,821.34 42,190.10 398,438 11 -519,714.84 -15,819.49 -150,381 128,188,873.52 153,325.68 1,452,935 13 3,866,475.77 -77,009.64 -741,376 1411,899,267.99 -133,998.0 -1,297,540 15 -1,622,486.43 -35,278.46 -334,685SUM 33,449,285.73 38,558.47 319,664.33 NPV ($) DV01 CV01 CS33,449,285.73 38,558.47 319,664.33

Table 2 also includes columns for DV01 and CV01 values. A DV01 value isa dollar value of a basis point and reflects a change in swap presentvalue resulting from a one basis point shift in a swap curve. The CV01value is the portion of the price change in the actual swap that is notreflected in the DV01 value. Because DV01 is a linear estimate of pricechange, there will be a gap between the actual price change of a convexinstrument like a swap and a DV01 estimate. This gap is estimated byCV01, the second measure of price sensitivity. Put another way, DV01 isthe first derivative of price/yield and CV01 is the second derivative.DV01 and CV01 are two metrics often used to assess risk of a swap. Asseen in Table 2, the DV01 value for the compressed swap is equal to thesum of the DV01 values of swaps 1 through 15. Similarly, the CV01 valuefor the compressed swap is equal to the sum of the CV01 values of swaps1 through 15.

Additional aspects of the above-described compression method are alsonotable. In some embodiments, the fixed rate x_(B) of the compressedswap may be determined using techniques other than by a simple average.As the amount of the amount of the fixed rate x_(B) varies, other valueswill be affected as indicated in Table 3.

TABLE 3 x_(B) rises x_(B) falls N_(B) falls rises c rises fallscompressed swap net present value falls rises compressed swap up-frontpayment/notional rises falls

Returning to FIG. 2 , in step 203 module 140 determines a neededprecision for the value c. In some embodiments, certain aspects ofcomputer system 100 or another computer system performing operations inconnection with a compressed swap may only be capable of deliveringmessages or otherwise processing with a fixed precision (e.g., sixdigits). However, there may be no such limitation on the types of swapsthat may be in a given portfolio, and parties may enter into swaps thatspecify fixed rates using more digits than are supported by some aspectsof computer system 100. This may lead to unacceptable imprecision. Forexample, it may be necessary to specify a compressed swap floating rate(f_(G) + c) with ten digits in order for the net present value and riskof the compressed swap to be equivalent to m swaps in a portfolio. Ifthe floating rate is truncated or rounded to six digits when calculatinga performance bond requirement, that requirement may be based on ahypothetical swap that less accurately models the risk and net presentvalue of actual swaps in the portfolio.

In some embodiments, module 140 determines required precision usingEquation 4.

$D = \left\lfloor {\log\left( \frac{1}{\left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}\left( {\sum_{j = 1}^{m}{N_{j} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}}} \right)}}} \right\rbrack}{\sum_{g = 1}^{G}{df_{g}dt_{g}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}}} \right| - c} \right)} \right\rfloor$

In Equation 4, and in subsequently described equations and inequalities,D is an integer value representing the number of digits of neededprecision necessary for the compressed swap to accurately model the riskand net present values of the m swaps, E is a value chosen to limit thedifference between net present value of the compressed swap and thecombined net present values of the m swaps, and the “[ ]” bracketsrepresent a floor function in which the result is the largest integervalue less than or equal to the argument within those brackets. In someembodiments, E equals 0.01. Derivation of Equation 4 is explained below.

In step 204, module 140 determines if the required precision D isgreater than the lowest precision D_(A) available in one or morecomponents of computer system 100 that will take action based on thecompressed swap. In some embodiments, for example, a module 140 may havethe ability to perform computations using a precision equal to orgreater than D, but other components of module 140 (e.g., hardwareand/or software portions of module 140 that determine performance bondrequirements and/or compliance with such requirements) may only be ableto send or receive messages having data values with precision D_(A) thatmay be less than D. If module 140 determines in step 204 that therequired precision D is not greater than the available precision D_(A),the method proceeds to step 206 on the “no” branch. Step 206 isdiscussed below. If module 140 determines that the required precision Dis greater than the available precision D_(A), the method proceeds tostep 205 on the “yes” branch.

In step 205, module 140 identifies parameters c₁ and N_(B1) for a firstdisaggregated swap to represent a first portion of the compressed swapand parameters c₂ and N_(B2) for a second disaggregated swap torepresent a second portion of the compressed swap. In some embodiments,module 140 selects a c₁ value that is greater than the c value butlimited to the available precision, as well as a c₂value that is lessthan the c value but limited to the available precision. In someembodiments, module 140 calculates c₁ by truncating c after the D_(A)^(th) decimal and increasing the D_(A) ^(th) decimal by 1 and calculatesc₂ by truncating c after the D_(A) ^(th) decimal and decreasing theD_(A) ^(th) decimal by 1. For example, if D = 10, D_(A) = 6, and c =0.531296742, then c₁ = 0.53130 and c₂= 0.53128. Also in step 205, module140 selects values N_(B1) and N_(B2) such that c₁*N_(B1) + c₂*N_(B2) =c*N_(B), with N_(B1) + N_(B2) = N_(B). Continuing the example, andassuming N_(B) = $1,000,000, N_(B1) = $837,100 and N_(B2) = $162,900.

At the conclusion of step 205, module 140 defines the firstdisaggregated compressed swap based on x_(B), c₁, and N_(B1), i.e.,hypothetically receive fixed rate payments at rate x_(B) on notionalN_(B1) and make floating rate payments at (f_(g) + c₁) if N_(B1) ispositive or hypothetically make fixed rate payments at rate x_(B) onnotional N_(B1) and receive floating rate payments at (f_(g) + c₁) ifN_(B1) is negative. Module 140 similarly defines the seconddisaggregated compressed swap based on x_(B), c₂, and N_(B2). The summednet present value and risk of the first and second disaggregatedcompressed swaps are equivalent to the net present value and risk of thecompressed swap.

In step 207, in some cases, module 140 may be used to determine aperformance bond requirement based on the first and second disaggregatedcompressed swaps. In some embodiments, a performance bond may be adeposit of cash or other value that a holder of the portfolio includingthe m swaps must place on deposit in an account of the entity thatoperates computer system 100. In other embodiments, a performance bondmay represent a minimum capital requirement that the portfolio holdermust satisfy, but which may not necessarily be in the form of a depositwith the entity that operates computer system 100. The operations ofstep 206 may be similar to those of conventional methods for determininga performance bond requirement for a swap or portfolio of swaps, butwith such methods being performed with regard to the first and seconddisaggregated compressed swaps instead of the m actual swaps.

If the “no” branch was taken from step 204, module 140 determines aperformance bond requirement in step 206 based on the compressed swap.As in step 207, the operations of step 206 may be similar to those inconventional methods for determining a performance bond requirement fora swap or portfolio of swaps, but with such methods being performed withregard to the compressed swap instead of the m actual swaps.

From either step 206 or 207, module 140 proceeds to step 208. In step208, module 140 compares the determined performance bond requirementwith account data for the holder of the portfolio that includes the mswaps. In some embodiments, that account data may include a balance of adeposit account maintained by the portfolio holder in an accountdesignated to hold performance bond funds. In some embodiments, thataccount data may also or alternatively include data reflecting whetherthe portfolio holder has submitted evidence to show sufficientcapitalization (e.g., through deposits or assets located elsewhere).

In step 209, and based on the comparison of step 208, module 140 takesadditional action. That action may include, for example, confirming thatthe performance bond requirement is satisfied and storing dataindicating that satisfaction. That action may alternatively include,based on determining in step 208 that the performance bond requirementis not satisfied, transmitting a communication to the portfolio holderregarding a requirement for amounts on deposit, capitalization, and/orother security to fulfil the performance bond requirement, and/orpreventing further trading or other activity until such requirement isfulfilled.

FIG. 4 is a flow chart showing operations performed by computer system100, according to some additional embodiments, in connection withcalculating parameters for a hypothetical condensed swap. In theembodiment of FIG. 4 , disaggregated compressed swaps are notconsidered. Steps 401 through 405 are respectively similar to steps 201,202, 206, 208, and 209 of FIG. 2 .

NPV of Compressed Swap and of M Swaps

In general, a net present value S of each of the m swaps can bedescribed by Equation 5.

$S_{j} = N_{j}\left( {x_{j}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i} + {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}}} \right)$

In Equation 5, and in subsequently described equations and inequalities,n is the number of fixed rate payment periods for the j^(th) swap, i isan index to one of the n fixed rate payment periods, dfi is the fixedrate discount factor applicable to the i^(th) fixed rate payment period,and dti is the duration of i^(th) fixed rate payment period. Equation 5is based on a convention in which a notional value is positive for afixed rate receiver and negative for a fixed rate payer.

The sum of the net present values for each of the m swaps, S₁ + S₂ + ...+S_(m) can be represented as shown below in Equations 6.

$\begin{matrix}{S_{1} + S_{2} + \cdots + S_{m} =} \\{N_{1}\left( {x_{1}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right) +} \\{\cdots + N_{m}\left( {x_{m}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i} + {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}}} \right)} \\ = \\{N_{1}x_{1}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i} + N_{1}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g} + \cdots + N_{m}x_{m}}}}}} \\{\sum\limits_{i = 1}^{n}{df_{i}dt_{i} + N_{m}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}} \\ = \\{N_{1}x_{1}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i} + \cdots + N_{m}x_{m}}}} \\{\sum\limits_{i = 1}^{n}{df_{i}dt_{i} + N_{1}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g} + \cdots}}}} \\{+ N_{m}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g} =}}} \\{{\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i} + {\sum\limits_{j = 1}^{m}{N_{j}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}}}}}\end{matrix}$

The net present value of a compressed swap having parameters x_(B),N_(B), and c as set forth in Equations 1 through 3 can be represented byEquation 7.

$S_{B} = N_{B}\left( {x_{B}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{g = 1}^{G}{\left( {f_{g} + c} \right)df_{g}dt_{g}}}} \right)$

As shown below in Equations 8, the net present value of the compressedswap is the same as the sum of the net present values of the m swaps.

$\begin{array}{l}{S_{B} = N_{B}\left( {x_{B}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{g = 1}^{G}{\left( {f_{g} + c} \right)df_{g}dt_{g}}}} \right)} \\{= \frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{\frac{1}{m}{\sum_{j = 1}^{m}x_{j}}}\left( {\frac{1}{m}{\sum\limits_{j = 1}^{m}x_{j}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}} + c{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}}} \right)} \\{= \frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{\frac{1}{m}{\sum_{j = 1}^{m}x_{j}}}\left( {\frac{1}{m}{\sum\limits_{j = 1}^{m}x_{j}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}}} \right)} \\{+ {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \\{+ \left( \frac{1}{\sum_{g = 1}^{G}{df_{g}dt_{g}}} \right)\left\lbrack \frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}} \right)} \\{\left( \left( {- {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right\rbrack \right)\left( {\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}} \right)} \\{= \frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{\frac{1}{m}{\sum_{j = 1}^{m}x_{j}}}\left( {\frac{1}{m}{\sum\limits_{j = 1}^{m}x_{j}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}}} \right)} \\{+ {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}} + \frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}} \\\left( {- {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right) \\{= \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \\\left( {\frac{1}{m}{\sum\limits_{j = 1}^{m}x_{j}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + \frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}} \right) \\{= \left( {\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{1}{m}{\sum\limits_{j = 1}^{m}x_{j}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}}} \right)} \\\left( {+ \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}} \right) \\{= \left( {{\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right)} \\{= {\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}\end{array}$

The last line of Equations 8 is the same as the alternate expression ofthe summed net present values of the m swaps shown in the last line ofEquations 6.

Derivation of Equation 3

The second term in the last line of Equations 6

$\left( {{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right)$

represents a sum of the present values of the floating rate legs of them swaps. As shown below in Equations 9a through 9g, Equation 3 can bederived by assuming that the floating leg of the compressed swap, whichhas a notional N_(B) and floating rate (f_(g) + c), has a present valueequal to the present value of the floating rate legs of the m swaps, andthen solving for c:

$N_{B}{\sum\limits_{g = 1}^{G}{\left( {f_{g} + c} \right)df_{g}dt_{g}}} = {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}$

$\frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{\frac{1}{m}{\sum_{j = 1}^{m}x_{j}}}{\sum\limits_{g = 1}^{G}{\left( {f_{g} + c} \right)df_{g}dt_{g}}} = {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}$

${\sum\limits_{g = 1}^{G}{\left( {f_{g} + c} \right)df_{g}dt_{g}}} = \frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}$

${\sum\limits_{g = 1}^{G}\left( {f_{g}df_{g}dt_{g} + cdf_{g}dt_{g}} \right)} = \frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}$

${\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}} + {\sum\limits_{g = 1}^{G}{cdf_{g}dt_{g}}} = \frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}$

$c{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}} = \frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}} - {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}$

$c = \frac{1}{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\left\lbrack {\frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}} - {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right\rbrack$

Derivation of Equation 4

As can be seen in Equations 8, the net present value of the sum of the mswaps is equal to the net present value of the compressed swap. This canbe rewritten as shown below in Equation 10.

$\begin{array}{l}{{\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \\{= N_{B}\left( {x_{B}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{g = 1}^{G}{\left( {fg + c} \right)df_{g}dt_{g}}}} \right)}\end{array}$

Limiting the precision of a value of c to D decimal places can berepresented as:

$\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor$

Limiting a difference between a sum of net present values for the mswaps (left side of Equation 10) and a net present value of a compressedswap (right side of Equation 10) to a value E when the precision of c islimited to D can be represented by Inequality 1:

$\begin{array}{l}\left| {{\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right) \\{\left( {- N_{B}\left( {x_{B}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{}^{}{\left( {f_{g} + \frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor} \right)df_{g}dt_{g}}}} \right)} \right| < E}\end{array}$

If E is set to 0.01, Inequality 1 represents a requirement that theprecision D be such that the difference between the sum of net presentvalues for the m swaps and a net present value of a compressed swap(with c having precision D) be less than one cent. Inequalities 2athrough 2s show how Inequality 1 results in Equation 4.

$\begin{array}{l}\left| {{\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right) \\{- m\frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{\sum_{j = 1}^{m}x_{j}}\left( {\frac{1}{m}{\sum\limits_{j = 1}^{m}x_{j}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{g = 1}^{G}{fdf_{g}dt_{g}}}} \right)} \\{\left( \left( {+ {\sum\limits_{g = 1}^{G}{\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor df_{g}dt_{g}}}} \right) \right| < E}\end{array}$

(Note: Inequality 2a is similar to Inequality 1, but with x_(B) andN_(B) replaced by the expressions from Equations 1 and 2.)

$\begin{array}{l}\left| {{\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right) \\{- m\frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{\sum_{j = 1}^{m}x_{j}}\left( {\frac{1}{m}{\sum\limits_{j = 1}^{m}x_{j}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{g = 1}^{G}{fdf_{g}dt_{g}}}} \right)} \\{\left( \left( {+ \frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}}} \right) \right| < E}\end{array}$

$\begin{array}{l}\left| {{\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}} -} \right) \\{\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{\sum_{j = 1}^{m}x_{j}}{m}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}}} \\{- \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}{\sum\limits_{g = 1}^{G}{fdf_{g}dt_{g}}}} \\{\left( {- \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}}} \right| < E}\end{array}$

$\begin{array}{l}{\left| {{\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}{\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}} + {\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}} - {\sum\limits_{j = 1}^{m}{N_{j}x_{j}}}} \right){\sum\limits_{i = 1}^{n}{df_{i}dt_{i}}}} \\{- \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}{\sum\limits_{g = 1}^{G}{fdf_{g}dt_{g}}}} \\{\left( {- \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}}} \right| < E}\end{array}$

$\begin{array}{l}\left| {{\sum\limits_{j = 1}^{m}N_{j}}{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}{\sum\limits_{g = 1}^{G}{fdf_{g}dt_{g}}}} \right) \\{\left( {- \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}}} \right| < E}\end{array}$

$\begin{array}{l}\left| {{\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum\limits_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right) \\{\left( {- \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}}} \right| < E}\end{array}$

$\begin{array}{l}{- E < {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum\limits_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \\{- \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}} < E}\end{array}$

$\begin{array}{l}{- E - {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum\limits_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \\{< - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}}} \\{< E - {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum\limits_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)}\end{array}$

$\begin{array}{l}{- E - {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum\limits_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \\{< - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor{\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}}} \\{< E - {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum\limits_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)}\end{array}$

$\begin{array}{l}{- E - {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum\limits_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \\{< - {\sum\limits_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor} \\{< E - {\sum\limits_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum\limits_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)}\end{array}$

$\begin{array}{l}{- \frac{\left\lbrack {- E - {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} > \frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor} \\{> - \frac{\left\lbrack {E - {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}}}\end{array}$

$\begin{array}{l}{\frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} > \frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor} \\{> \frac{\left\lbrack {- E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}}}\end{array}$

$\frac{1}{10^{D}}\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor < \left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right|$

$\frac{1}{10^{D}}\left( {10^{D}c + 1} \right) < \left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right|$

(Note: Inequality 2n, in comparison to Inequality 2m, reflects the factthat

$\left\lfloor {10^{D}c + \frac{1}{2}} \right\rfloor \leq \left( {10^{D}c + 1} \right)\left( . \right)$

$\left( {c + \frac{1}{10^{D}}} \right) < \left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right|$

$\frac{1}{10^{D}} < \left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right| - c$

$10^{D} > \frac{1}{\left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {\sum_{j = 1}^{m}{N_{j} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right| - c}$

$D\log(10) > \log\left( \frac{1}{\left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}\left( {\sum_{j = 1}^{m}{N_{j} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}}} \right)}}} \right\rbrack}{\sum_{g = 1}^{G}{df_{g}dt_{g}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}}} \right| - c} \right)$

$D > \log\left( \frac{1}{\left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {\sum_{j = 1}^{m}{N_{j} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right| - c} \right)$

$D = \left\lfloor {\log\left( \frac{1}{\left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {\sum_{j = 1}^{m}{N_{j} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right| - c} \right)} \right\rfloor$

In any of the above aspects, the various features may be implemented inhardware, or as software modules running on one or more processors.Features of one aspect may be applied to any of the other aspects.

There may also be provided a computer program or a computer programproduct for carrying out any of the methods described herein, and acomputer readable medium having stored thereon a program for carryingout any of the methods described herein. A computer program may bestored on a computer-readable medium, or it could, for example, be inthe form of a signal such as a downloadable data signal provided from anInternet website, or it could be in any other form.

Conclusion

The foregoing description of embodiments has been presented for purposesof illustration and description. The foregoing description is notintended to be exhaustive or to limit embodiments to the precise formexplicitly described or mentioned herein.

Modifications and variations are possible in light of the aboveteachings or may be acquired from practice of various embodiments. Theembodiments discussed herein were chosen and described in order toexplain the principles and the nature of various embodiments and theirpractical application to enable one skilled in the art to make and usethese and other embodiments with various modifications as are suited tothe particular use contemplated. Any and all permutations of featuresfrom above-described embodiments are the within the scope of theinvention.

We claim:
 1. A method comprising: performing, automatically by acomputer system when the data size of data corresponding to a portfoliocomprising a plurality of interest rate swaps, each being characterizedby a risk value, exceeds a defined data storage capacity of anon-transitory memory device in which the data is stored: calculating,by the computer system, one or more replacement swaps having a combinedrisk value equivalent to a sum of the risk values of each of at least asubset of the plurality of interest rate swaps of the portfolio;forming, by the computer system, replacement data corresponding to areplacement portfolio comprising the one or more replacement swaps inplace of the subset of the plurality of interest rate swaps of theportfolio; and replacing, by the computer system, the data comprisingthe portfolio with the replacement data in the non-transitory memorydevice to reduce a data storage requirement of the portfolio therein. 2.The method of claim 1, wherein the one or more replacement swapscomprise at least two replacement swaps when the computer systemdetermines that a data value precision of the sum of the risk values ofeach of at least a subset of the plurality of interest rate swaps of theportfolio exceeds a data value precision of at least one component ofthe computer system which prevents the computer system from calculatingless than the at least two replacement swaps having a combined riskvalue equivalent to the sum of the risk values of each of at least asubset of the plurality of interest rate swaps of the portfolio.
 3. Themethod of claim 1, further comprising: determining, by the computersystem, a performance bond requirement attributable to the plurality ofinterest rate swaps; comparing, by the computer system, the performancebond requirement to account data associated with a holder of theportfolio; performing, by the computer system, one or more additionalactions based on the comparing comprising at least one of (i) storingdata regarding satisfaction of the performance bond requirement, and(ii) transmitting a communication regarding the performance bondrequirement.
 4. The method of claim 1, wherein calculating, for each ofthe one or more replacement swaps, a replacement swap fixed rate valuex_(B), a replacement swap notional value N_(B), and a replacement swapfloating rate spread value c according to$x_{B} = \frac{1}{m}{\sum_{j = 1}^{m}x_{j}},$$N_{B} = \frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{x_{B}},\text{and}$$\begin{array}{l}{c = \frac{1}{\sum_{g = 1}^{G}{df_{g}dt_{g}}}} \\{\left\lbrack {\frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}} - {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}} \right\rbrack,\text{and}}\end{array}$ x_(j) is a fixed rate value for the j^(th) interest rateswap, wherein m is the number of interest rate swaps in the plurality ofinterest rate swaps, N_(j) is a notional value of the j^(th) interestrate swap, G is the number of floating rate payment periods in thecommon tenor, f_(g) is a floating rate value corresponding to the g^(th)floating rate payment period, df_(g) is a floating rate discount factorcorresponding to the g^(th) floating rate payment period, and dt_(g) isa duration of the g^(th) floating rate payment period.
 5. The method ofclaim 1, wherein a DV01 value for the one or more replacement swaps isthe same as a sum of DV01 values for the plurality of interest rateswaps, and a CV01 value for the one or more replacement swaps is thesame as a sum of CV01 values for the plurality of interest rate swaps.6. The method of claim 1, further comprising: determining a performancebond requirement of the plurality of interest rate swaps based on firstand second disaggregated swaps, the first disaggregated swap comprises areplacement swap fixed rate value x_(B), a first disaggregated swapnotional value N_(B1), and a first disaggregated swap spread value c₁,and the second disaggregated swap comprises the replacement swap fixedrate value x_(B), a second disaggregated swap notional value N_(B2), anda second disaggregated swap spread value c₂, and further comprising:determining a required precision for the floating rate spread value c;determining the required precision is greater than an availableprecision; based on the determining that the required precision isgreater than an available precision, selecting a c₁ value greater thanthe c value and a c₂ value less than the c value; and determining N_(B1)and N_(B2) values such N_(B1)*c₁ + N_(B2)*c₂ = N_(B)*c and such thatN_(B1) + N_(B2) = N_(B).
 7. The method of claim 6, wherein: determiningthe required precision comprises determining the required precisionaccording to $\begin{array}{l}{D =} \\{\left\lfloor {\log\left( \frac{1}{\left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right| - c} \right)} \right\rfloor,\text{and}}\end{array}$ D is the required precision, E is a constant chosen tolimit a difference between a present value of the one or morereplacement swaps and combined present values of the plurality ofinterest rate swaps, m is the number of interest rate swaps in theplurality of interest rate swaps, x_(j) is a fixed rate value for thej^(th) interest rate swap, N_(j) is a notional value of the j^(th)interest rate swap, G is the number of floating rate payment periods inthe common tenor, f_(g) is a floating rate value corresponding to theg^(th) floating rate payment period, df_(g) is a floating rate discountfactor corresponding to the g^(th) floating rate payment period, anddt_(g) is a duration of the g^(th) floating rate payment period.
 8. Anon-transitory computer-readable media storing computer executableinstructions that, when executed, cause a computer system to performoperations that include: performing, automatically by a computer systemwhen the data size of data corresponding to a portfolio comprising aplurality of interest rate swaps, each being characterized by a riskvalue, exceeds a defined data storage capacity of a non-transitorymemory device in which the data is stored: calculating, by the computersystem, one or more replacement swaps having a combined risk valueequivalent to a sum of the risk values of each of at least a subset ofthe plurality of interest rate swaps of the portfolio; forming, by thecomputer system, replacement data corresponding to a replacementportfolio comprising the one or more replacement swaps in place of thesubset of the plurality of interest rate swaps of the portfolio; andreplacing, by the computer system, the data comprising the portfoliowith the replacement data in the non-transitory memory device to reducea data storage requirement of the portfolio therein.
 9. The one or morenon-transitory computer-readable media of claim 8, wherein the one ormore replacement swaps comprise at least two replacement swaps when thecomputer system determines that a data value precision of the sum of therisk values of each of at least a subset of the plurality of interestrate swaps of the portfolio exceeds a data value precision of at leastone component of the computer system which prevents the computer systemfrom calculating less than the at least two replacement swaps having acombined risk value equivalent to the sum of the risk values of each ofat least a subset of the plurality of interest rate swaps of theportfolio.
 10. The one or more non-transitory computer-readable media ofclaim 8, wherein the computer executable instructions are furtherexecutable to cause the computer system to perform operations thatinclude: determining, based at least in part on the combined risk valueof the one or more replacement swaps, a performance bond requirementattributable to the plurality of interest rate swaps; comparing theperformance bond requirement to account data associated with a holder ofthe portfolio; performing one or more additional actions based on thecomparing comprising at least one of (i) storing data regardingsatisfaction of the performance bond requirement, and (ii) transmittinga communication regarding the performance bond requirement.
 11. The oneor more non-transitory computer-readable media of claim 8, wherein thecomputer executable instructions are further executable to cause thecomputer system to perform operations that include: calculating, foreach of the one or more replacement swaps, a replacement swap fixed ratevalue x_(B), a replacement swap notional value N_(B), and a replacementswap floating rate spread value c according to$x_{B} = \frac{1}{m}{\sum_{j = 1}^{m}x_{j}},$$N_{B} = \frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{x_{B}},\text{and}$$\begin{array}{l}{c = \frac{1}{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\left\lbrack {\frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}} -} \right)} \\{\left( {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}} \right\rbrack,\text{and}}\end{array}$ x_(j) is a fixed rate value for the j^(th) interest rateswap, wherein m is the number of interest rate swaps in the plurality ofinterest rate swaps, N_(j) is a notional value of the j^(th) interestrate swap, G is the number of floating rate payment periods in thecommon tenor, f_(g) is a floating rate value corresponding to the g^(th)floating rate payment period, df_(g) is a floating rate discount factorcorresponding to the g^(th) floating rate payment period, and dt_(g) isa duration of the g^(th) floating rate payment period.
 12. The one ormore non-transitory computer-readable media of claim 8, wherein a DV01value for the one or more replacement swaps is the same as a sum of DV01values for the plurality interest rate swaps, and a CV01 value for theone or more replacement swaps is the same as a sum of CV01 values forthe plurality of interest rate swaps.
 13. The one or more non-transitorycomputer-readable media of claim 8, wherein the computer executableinstructions are further executable to cause the computer system toperform operations that include: determining a performance bondrequirement of the plurality of interest rate swaps based on first andsecond disaggregated swaps, the first disaggregated swap comprises areplacement swap fixed rate value x_(B), a first disaggregated swapnotional value N_(B1), and a first disaggregated swap spread value c₁,and the second disaggregated swap comprises the replacement swap fixedrate value x_(B), a second disaggregated swap notional value N_(B2), anda second disaggregated swap spread value c₂, and further comprisingstored computer executable instructions that, when executed, cause thecomputer system to perform operations that include: determining arequired precision for the floating rate spread value c; determining therequired precision is greater than an available precision; based on thedetermining that the required precision is greater than an availableprecision, selecting a c₁ value greater than the c value and a c₂ valueless than the c value; and determining N_(B1) and N_(B2) values suchN_(B1)*c₁ + N_(B2)*_(C2) = N_(B)*c and such that N_(B1) + N_(B2) =N_(B).
 14. The one or more non-transitory computer-readable media ofclaim 13, wherein: determining the required precision comprisesdetermining the required precision according to $\begin{array}{l}{D =} \\{\left\lfloor {\log\left( \frac{1}{\left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right| - c} \right)} \right\rfloor,\text{and}}\end{array}$ D is the required precision, E is a constant chosen tolimit a difference between a present value of the one or morereplacement swaps and combined present values of the plurality ofinterest rate swaps, m is the number of interest rate swaps in theplurality of interest rate swaps, x_(j) is a fixed rate value for thej^(th) interest rate swap, N_(j) is a notional value of the j^(th)interest rate swap, G is the number of floating rate payment periods inthe common tenor, f_(g) is a floating rate value corresponding to theg^(th) floating rate payment period, df_(g) is a floating rate discountfactor corresponding to the g^(th) floating rate payment period, anddt_(g) is a duration of the g^(th) floating rate payment period.
 15. Acomputer system comprising: a memory device having a defined storagecapacity; at least one processor coupled with the memory device; and atleast one non-transitory memory coupled with the processor, wherein theat least one non-transitory memory stores instructions that, whenexecuted, cause the processor to: perform, automatically when the datasize of data corresponding to a portfolio comprising a plurality ofinterest rate swaps, each being characterized by a risk value, exceeds adefined data storage capacity of a non-transitory memory device in whichthe data is stored: calculate one or more replacement swaps having acombined risk value equivalent to a sum of the risk values of each of atleast a subset of the plurality of interest rate swaps of the portfolio;form replacement data corresponding to a replacement portfoliocomprising the one or more replacement swaps in place of the subset ofthe plurality of interest rate swaps of the portfolio; and replace thedata comprising the portfolio with the replacement data in thenon-transitory memory device to reduce a data storage requirement of theportfolio therein.
 16. The computer system of claim 15, wherein the oneor more replacement swaps comprise at least two replacement swaps whenthe computer system determines that a data value precision of the sum ofthe risk values of each of at least a subset of the plurality ofinterest rate swaps of the portfolio exceeds a data value precision ofat least one component of the computer system which prevents thecomputer system from calculating less than the at least two replacementswaps having a combined risk value equivalent to the sum of the riskvalues of each of at least a subset of the plurality of interest rateswaps of the portfolio.
 17. The computer system of claim 15, wherein theinstructions are further executable to cause the processor to :determine, based at least in part on the combined risk value of the oneor more replacement swaps, a performance bond requirement attributableto the plurality of interest rate swaps; compare the performance bondrequirement to account data associated with a holder of the portfolio;performing one or more additional actions based on the comparingcomprising at least one of (i) storing data regarding satisfaction ofthe performance bond requirement, and (ii) transmitting a communicationregarding the performance bond requirement.
 18. The computer system ofclaim 15, wherein the instructions are further executable to cause theprocessor to perform operations that include: calculating, for each ofthe one or more replacement swaps, a replacement swap fixed rate valuex_(B), a replacement swap notional value N_(B), and a replacement swapfloating rate spread value c according to$x_{B} = \frac{1}{m}{\sum_{j = 1}^{m}x_{j}},$$N_{B} = \frac{\sum_{j = 1}^{m}{N_{j}x_{j}}}{x_{B}},\text{and}$$\begin{array}{l}{c = \frac{1}{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\left\lbrack {\frac{{\sum_{j = 1}^{m}x_{j}}{\sum_{j = 1}^{m}N_{j}}{\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}}{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}} -} \right)} \\{\left( {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}} \right\rbrack,\text{and}}\end{array}$ x_(j) is a fixed rate value for the j^(th) interest rateswap, wherein N_(j) is a notional value of the j^(th) interest rateswap, wherein m is the number of interest rate swaps in the plurality ofinterest rate swaps, G is the number of floating rate payment periods inthe common tenor, f_(g) is a floating rate value corresponding to theg^(th) floating rate payment period, df_(g) is a floating rate discountfactor corresponding to the g^(th) floating rate payment period, anddt_(g) is a duration of the g^(th) floating rate payment period.
 19. Thecomputer system of claim 15, wherein a DV01 value for the one or morereplacement swaps is the same as a sum of DV01 values for the pluralityof interest rate swaps, and a CV01 value for the one or more replacementswaps is the same as a sum of CV01 values for the plurality of interestrate swaps.
 20. The computer system of claim 15, wherein theinstructions are further executable to cause the processor to performoperations that include: determining a performance bond requirementattributable to the plurality of interest rate swaps based on first andsecond disaggregated swaps, the first disaggregated swap comprises areplacement swap fixed rate value x_(B), a first disaggregated swapnotional value N_(B1), and a first disaggregated swap spread value c₁,and the second disaggregated swap comprises the replacement swap fixedrate value x_(B), a second disaggregated swap notional value N_(B2), anda second disaggregated swap spread value c₂, and wherein the at leastone non-transitory memory stores instructions that, when executed, causethe computer system to perform operations that include determining arequired precision for the floating rate spread value c, determining therequired precision is greater than an available precision, based on thedetermining that the required precision is greater than an availableprecision, selecting a c₁ value greater than the c value and a c₂ valueless than the c value, and determining N_(B1) and N_(B2) values suchN_(B1)*c₁ + N_(B2)*c₂ = N_(B)*c and such that N_(B1) + N_(B2) = N_(B).21. The computer system of claim 20, wherein the instructions arefurther executable to cause the processor to perform operations thatinclude: determining the required precision comprises determining therequired precision according to $\begin{array}{l}{D =} \\{\left\lfloor {\log\left( \frac{1}{\left| \frac{\left\lbrack {E + {\sum_{g = 1}^{G}{f_{g}df_{g}dt_{g}}}\left( {{\sum_{j = 1}^{m}N_{j}} - \frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right)} \right\rbrack}{{\sum_{g = 1}^{G}{df_{g}dt_{g}}}\frac{m{\sum_{j = 1}^{m}{N_{j}x_{j}}}}{\sum_{j = 1}^{m}x_{j}}} \right| - c} \right)} \right\rfloor,\text{and}}\end{array}$ D is the required precision, E is a constant chosen tolimit a difference between a present value of the one or morereplacement swaps and combined present values of the plurality ofinterest rate swaps, m is the number of interest rate swaps in theplurality of interest rate swaps, x_(j) is a fixed rate value for thej^(th) interest rate swap, N_(j) is a notional value of the j^(th)interest rate swap, G is the number of floating rate payment periods inthe common tenor, f_(g) is a floating rate value corresponding to theg^(th) floating rate payment period, df_(g) is a floating rate discountfactor corresponding to the g^(th) floating rate payment period, anddt_(g) is a duration of the g^(th) floating rate payment period.